The Active Shape Model (“ASM”) is an effective method for automated object boundary detection during image analysis. The ASM affords robust detection of the desired boundary by limiting the search space to high probability shapes. These attributes have enabled the successful utilization of the ASM across a variety of fields. Various techniques to extend the ASM to increase object recognition performance have also been proposed; however, the models may still fail in high noise environments or regions in which numerous structures present multiple confounding edges.
Object Boundary Detection
The general problem of object boundary detection in an image is well known in the art. The object is typically identified by finding a contour that minimizes an image “energy function.” The energy function is typically lowest when the contour lies close to the edge of the desired object.
Active Shape Models
The general active shape model approach has been well described, and is known in the art. ASMs utilize statistical models of shapes to control the iterative deformation of the contour while minimizing the image energy function. The statistical model is derived from a set of training shapes. For example, see The Use of Active Shape Models for Locating Structures in Medical Images, Image and Vision Computing, Vol. 12, No. 6, July 1994, pp. 355-366, which is hereby incorporated by reference in its entirety (hereinafter, Cootes et al.).
Briefly, the shape of an object may be represented by a set of points. An mD-dimensional vector x describing m points in D-dimensional space describes the shape of an object within an image. These points may correspond to, for example, well-defined landmarks or regularly spaced points on the boundary of the object. It is further assumed that this shape vector is more compactly represented as
                              x          =                                    x              0                        +                                          ∑                                  n                  =                  1                                N                            ⁢                                                b                  n                                ⁢                                  p                  n                                                                    ,                            (        0        )            
where x0 is the mean shape, p1, . . . ,pN are orthonormal basis vectors and b1, . . . ,bN are scalar weights. Typically, only N basis vectors are used where N is much smaller than m, leading to a more compact representation. Object identification then comes down to optimizing the set of weights to minimize an image energy function.
Estimating appropriate values for the mean shape, x0, the basis vectors pn and the scalar weights bn is accomplished by examining the statistics of a training set of representative shapes (appropriately scaled and reoriented if desired). For example, a training set of images showing the carotid artery may be obtained wherein each image shows a cross-section of a carotid artery. On each image the location of the boundary of the carotid artery is carefully identified. An example of training set data for modeling the left ventricle of the heart is shown in Cootes et al.
Let μx and Kx be the sample mean and covariance matrix of the training set. Then, the mean shape x0 is defined to be equal to μx, and the basis vectors p1, . . . ,pN are taken to be the eigenvectors of Kx that correspond to the N largest eigenvalues of Kx. Additionally, the allowable range of weights bn are typically taken to be ±a√{square root over (λn)}, where λn is the corresponding eigenvalue and a is some scaling factor.
Any shape in the training set can be approximated using the sample mean and a weighted sum of the deviations obtained from the first N modes identified by the basis vectors corresponding to the largest eigenvalues. This also allows generation of new examples of shapes by varying the weights within suitable limits, so the new shapes will be similar to those in the training set. Therefore, suitable shapes for the object identified in new images (images not in the training set) can be obtained. This statistical model based on the training set of data can therefore be used to locate examples of objects in new images, using well-known procedures for minimizing the shape energy function. For example, estimating the location of points along the boundary of the shape, and using the model to move the points to best fit the image, as discussed in Cootes et al.
The original ASM formulation may be considered as composed of two components: 1) a shape model specification component, and 2) a new object detection component. A summary of the shape model specification is shown in FIG. 1, wherein the training shapes are provided 90 to the model, and the mean shape μx and covariance matrix Kx are calculated 92, as discussed above. The training shapes are shapes obtained from images for the class of objects or shapes that the ASM is intended to identify. In the example below, the training shapes are shapes of the outline of the carotid artery at selected axial locations. The eigenvalues λn of the covariance matrix, and the eigenvectors p1, . . . , pN corresponding to the largest N eigenvalues are then calculated 94. The mean shape μx 96 and eigenvalues λn and eigenvectors p1, . . . ,pN 98 are then used by the active shape model to identify the desired object shape in a non-training set image. The shape model specification component is then used using well-known techniques, in identifying instances of the object shape in images.
In taking this approach, there are three underlying assumptions of the shape model. First the shapes are random vectors. Second, the random vectors are drawn from a multivariate Gaussian probability density function. Third, in certain directions the regions of non-negligible probability are so thin that variation in those directions can be neglected. The shape model then takes advantage of the fact that any dependent multivariate Gaussian random variables can be transformed into a set of independent Gaussian random variables by identifying the principal axes of the Gaussian distribution. The eigenvectors of Kx yield the principal axes of the distribution. Discarding those that correspond to the mD-N smallest eigenvalues eliminates the negligibly thin dimensions, leaving the eigenvectors p1, . . . ,pN. The weights b1, . . . ,bN are the transformed, independent Gaussian random variables with mean 0 and variance λn. Assuming they lie within ±a√{square root over (λn)} amounts to confining them to ±a standard deviations of their means.